@Article{IJNAM-15-3,
author = {Robert, Altmann and Jan, Heiland},
title = {Regularization and Rothe Discretization of Semi-Explicit Operator DAEs},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2018},
volume = {15},
number = {3},
pages = {452--478},
abstract = {<p style="text-align: justify;">A general framework for the regularization of constrained PDEs, also called operator
differential-algebraic equations (operator DAEs), is presented. The given procedure works
for semi-explicit and semi-linear operator DAEs of first order including the Navier-Stokes and
other flow equations. The proposed reformulation is consistent, i.e., the solution of the PDE remains
untouched. Its main advantage is that it regularizes the operator DAE in the sense that
a semi-discretization in space leads to a DAE of lower index. Furthermore, a stability analysis
is presented for the linear case, which shows that the regularization provides benefits also for
the application of the Rothe method. For this, the influence of perturbations is analyzed for the
different formulations. The results are verified by means of a numerical example with an adaptive
space discretization.</p>},
issn = {2617-8710},
doi = {https://doi.org/2018-IJNAM-12525},
url = {https://global-sci.com/article/83121/regularization-and-rothe-discretization-of-semi-explicit-operator-daes}
}